Optical complex matrix-vector multiplication with negative binary inner products

Related Experiment Video

Updated: Jun 19, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

L Liu, G Li, Y Yin

    Optics Letters
    |October 27, 2009
    PubMed

    More Related Videos

    Generation and Coherent Control of Pulsed Quantum Frequency Combs06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    Related Concept Videos

    Vector Representation of Complex Numbers01:16

    Vector Representation of Complex Numbers

    Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
    Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.
    Scalar and Vector Triple Products01:06

    Scalar and Vector Triple Products

    Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
    The scalar triple product is the dot product of a vector with the cross product of two vectors.
    Complex Numbers01:29

    Complex Numbers

    The real number system cannot represent the square root of a negative number, which restricts solutions for certain equations, such as quadratics with negative discriminants. To address this, the complex number system was developed, introducing the imaginary unit i, where i = √(-1). This extension allows for the representation of all roots, including those involving negative radicands.A complex number is written in the form x + yi, where x and y are real numbers. Here, x represents the real...
    Dot Product of Two Vectors01:27

    Dot Product of Two Vectors

    The dot product, or scalar product, is a fundamental operation in vector algebra that combines two vectors to yield a scalar quantity. It is particularly valuable in physical applications, such as calculating work, and in mathematical contexts, such as determining vector projections and direction cosines.For vectors a = ⟨a₁, a₂, a₃⟩ and b = ⟨b₁, b₂, b₃⟩, the dot product is defined as:\begin{equation*}\mathbf{a} \cdot \mathbf{b} = a_1b_1 + a_2b_2 + a_3b_3\end{equation*}This operation is...
    Vector Product (Cross Product)01:17

    Vector Product (Cross Product)

    Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule.
    Consider the cross product of two vectors. Imagine rotating the first vector about...
    Vector Algebra: Method of Components01:08

    Vector Algebra: Method of Components

    It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
    In many applications, the magnitudes and directions of...